Consumer theory Totally Explained

Everything about Income Effect totally explained

Consumer theory is a theory of microeconomics that relates preferences to consumer demand curves. The models that make up consumer theory are used to represent prospectively observable demand patterns for an individual buyer on the hypothesis of constrained optimization. Prominent variables used to explain the amount demanded of a good are the price per unit of that good and money income of the consumer. A change in the price of a good is posited to change the amount demanded of that good in such a way that it can be broken down into two parts: the substitution effect and the income effect.

Model setup

For an individual, indifference curves and an assumption of constant prices and a fixed income in a two-good world will give the following diagram. The consumer can choose any point on or below the budget constraint line BC. This line is diagonal since it comes from the equation

xp_X + y p_Y leq mathrm

. In other words, the amount spent on both goods together is less than or equal to the income of the consumer. The consumer will choose the indifference curve with the highest utility that's within his budget constraint. Every point on I3 is outside his budget constraint so the best that he can do is the single point on I2 that's tangent to his budget constraint. He will purchase X* of good X and Y* of good Y.
Income effect and price effect deal with how the change in price of a commodity changes the consumption of the good. The theory of consumer choice examines the trade-offs and decisions people make in their role as consumers as prices and their income changes.

Substitution effect

Substitution effect is the effect observed through changes in relative price of goods.
   These curves can be used to predict the effect of changes to the budget constraint. The graphic below shows the effect of a price increase for good Y. If the price of Y increases, the budget constraint will pivot from BC2 to BC1. Notice that because the price of X doesn't change, the consumer can still buy the same amount of X if he or she chooses to buy only good X. On the other hand, if the consumer chooses to buy only good Y, he or she'll be able to buy less of good Y because its price has increased.
   To maximize the utility with the reduced budget constraint, BC1, the consumer will re-allocate consumption to reach the highest available indifference curve which BC1 is tangent to. As shown on the diagram below, that curve is I1, and therefore the amount of good Y bought will shift from Y2 to Y1, and the amount of good X bought to shift from X2 to X1. The opposite effect will occur if the price of Y decreases causing the shift from BC2 to BC3, and I2 to I3.
   If these curves are plotted for many different prices of good Y, a demand curve for good Y can be constructed. The diagram below shows the demand curve for good Y as its price varies. Alternatively, if the price for good Y is fixed and the price for good X is varied, a demand curve for good X can be constructed.

Income effect

Another important item that can change is the income of the consumer. The income effect is the phenomenon observed through changes in purchasing power. It shows the real income of a consumer.
Graphically, as long as the prices remain constant, changing the income will create a parallel shift of the budget constraint. Increasing the income will shift the budget constraint right since more of both can be bought, and decreasing income will shift it left.
Depending on the indifference curves the amount of a good bought can either increase, decrease or stay the same when income increases. In the diagram below, good Y is a normal good since the amount purchased increased as the budget constraint shifted from BC1 to the higher income BC2. Good X is an inferior good since the amount bought decreased as the income increases.

Delta y_1^n

is the change in the demand for good 1 when we change income from

m'

m

, holding the price of good 1 fixed at

p_1'

Delta y_1^n = y_1(p_1', m) - y_1(p_1',m').

Price effect as sum of substitution and income effects

Every price change can be decomposed into an income effect and a substitution effect; the price effect is the sum of substitution and income effects.
   The substitution effect is a price change that alters the slope of the budget constraint but leaves the consumer on the same indifference curve. In order words, it illustrates the consumer's new consumption basket after the price change while being compensated as to allow the consumer to be as happy as previously. By this effect, the consumer is posited to substitute toward the good that becomes comparatively less expensive.
   If the good in question is a normal good, then the income effect from the rise in purchasing power from a price fall reinforces the substitution effect. If the good is an inferior good, then the income effect will offset in some degree the substitution effect. If the income effect for an inferior good is sufficiently strong, the consumer will buy less of the good when it becomes less expensive, a Giffen good (commonly believed to be a rarity).
   In the figure, the substitution effect,

Delta y_1^s

, is the change in the amount demanded for

y

when the price of good

y

falls from

p_1

p_1'

(increasing purchasing power for

y

) and, at the same time, the money income falls from

m

m'

to keep the consumer at the same level of utility on

I1

Delta y_1^s = y_1(p_1', m') - y_1(p_1,m).

The substitution effect increases the amount demanded of good

y

from

y_1

y_s

. In the example, the income effect of the price fall in

y_1

partly offsets the substitution effect as the amount demanded of

y

goes from

y_s

y_2

. Thus, the price effect is the algebraic sum of the substitution effect and the income effect.

Labor-leisure tradeoff

Consumer theory can also be used to analyze a consumer's choice between leisure and labor. Leisure is considered one good (often put on the horizontal-axis) and consumption is considered the other good. Since a consumer has a finite and scarce amount of time, he must make a choice between leisure (which earns no income for consumption) and labor (which does earn income for consumption).
The previous model of consumer choice theory is applicable with only slight modifications. First, the total amount of time that an individual has to allocate is known as his time endowment, and is often denoted as T. The amount an individual allocates to labor (denoted L) and leisure (l) is constrained by T such that: ť :

l + L = T,!

or ť :

l + (T-l) = T,!

A person's consumption is the amount of labor they choose multiplied by the amount they're paid per hour of labor (their wage, often denoted w). Thus, the amount that a person consumes is: ť :

C = w(T-l),!

When a consumer chooses no leisure

(l=0)

then

T-l = T

and

C = wT

.
From this labor-leisure tradeoff model, the substitution and income effects of various changes in price caused by welfare benefits, labor taxation, or tax credits can be analyzed.

Further Information

Get more info on 'Income Effect'.

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